Having said that I do think Britain is stronger as a union rather than a set of degenerate principalities and I offer my thanks to all members of our islands who fought and died in our collective wars, including Ireland in WW1.
p.s. I am certain 'Britain' is stronger as a union, but I do not think combined strength is the most important factor in any relationship and I do not think that the union is to the greater benefit of the NATION States of Scotland or Wales. England is by far the largest partner in the Union and as a result can democratically dominate all issues in the United Kingdom and control all the resources.
My gut reaction is that Carolingian cavalry would be too archaic to accurately represent either English or Scots horse of circa 1300. Some of the Norman horse might pass for second rate armored horse, but the Norman shields would not be appropriate. Armorers were the "high tech" workers of their day, and even in Scotland it is unlikely they would have been more than a generation behind. Further, it should be remembered that a great many Scottish noble families had close ties with England, and may well have acquired their armor there. Of course second line horse would probably have worn inferior armor, but you also need to worry about changes in clothing styles in the 240 years since Hastings.
Emhars' Vikings and Strelets' and Emhars' Saxons could be used to represent highland and island Scots, although I don't think either lend themselves to the schiltrons used at Falkirk or Bannockburn.
Of course, if you follow the Mel Gibson School Of History, you can probably get away with whatever you want, as long as you paint the faces blue, and for the Battle of Stirling you don't even need the Brig...